Not sure I have followed the timeline correctly, but it seems the OP's second stage appeal (Reg.17) must have been submitted no later than 2nd May. The appeal body requested more information (?on 19th May) and the OP provided it (?on 2nd June). The appeal body then issued its rejection of the second stage appeal on 4th June.
Regulation 17(8A) of the penalty fares regs states that:
"If an appeal is against a penalty fare calculated in accordance with regulation 9(1A) or (4A), where the relevant Appeal Panel—
(a) ...; or
(b)fails to adhere to the time period specified in paragraph 6 of Schedule 2, the appellant is not liable to pay the penalty fare in question and is only liable to pay the full single fare applicable for their journey."
The paragraph referred to, Para.2 in Schedule 6, states that:
"Where an Appeal Panel receives an appeal under regulation 16 or 17, it must decide whether to allow or not allow the appeal before the end of the period of 21 days beginning with the day on which the appeal is received."
If it is correct that a period of some 35 days (2nd May to 4th June) elapsed between lodgment of the Reg.17 appeal and the appeal body's decision not to allow it, then that body has failed to decide the appeal within the period it was required to do so. That activates the consequences specified in Regulation 17(8A), i.e. the OP thereupon ceased to be liable to pay the penalty fare but remained liable to pay the full single fare applicable. The OP hasn't yet provided details of the "full single fare applicable", but it is likely to be the total amount said to be due on the penalty fare notice less the £100 penalty fare element. Whatever that full single fare is, it is now the sum the OP should pay to discharge the outstanding fare liability due. If payment of that amount is now sent to the train company, it should be accompanied by a letter (a copy of which the OP should retain) stating that full payment is enclosed of the amount now due as a consequence of the appeal body's failure to decide the appeal within the time allowed - and appropriate reference can be made to the relevant extracts from the penalty fares rules quoted above.
That appears to be the correct way for the OP to proceed according to my understanding of the penalty fares rules, and it is a conclusion that stands entirely distinct from the question of whether South Eastern Trains is prohibited from prosecuting the OP in consequence of the penalty fare having remained uncancelled following commencement of an appeal. I regret that in the strange legal shadow world we now occupy as result of the the Chief Magistrate's ruling referenced in
@KirkstallOne's post above, no assurance can now be offered that passengers in receipt of a penalty fare will not also find themselves faced with prosecution in connection with the same incident as led to the penalty fare's issue.
